Analytical approach for estimating ground deformation profile induced by normal faulting in undrained clay

2013 ◽  
Vol 50 (4) ◽  
pp. 413-422 ◽  
Author(s):  
Q.P. Cai ◽  
Charles W.W. Ng
Keyword(s):  
Ground Deformation ◽  
Error Function ◽  
Hanging Wall ◽  
Numerical Data ◽  
Theoretical Models ◽  
Failure Surface ◽  
Vertical Displacement ◽  
Normal Faulting ◽  
Soil Thickness ◽  
Undrained Shear

Although theoretical models have been developed to predict the location of the failure surface in soil induced by bedrock faulting, no analytical tool is available to estimate subsurface ground deformation. In this paper, a newly developed semi-empirical approach is introduced and developed for calculating surface and subsurface deformations induced by normal faulting in undrained clay. Based on observations from centrifuge model tests, the ground deformation mechanisms are identified by three regions; namely, a stationary zone, a shearing zone, and a rigid body zone. By using an error function to represent vertical displacement continuously, the ground deformation profile can be described quantitatively. It is revealed that the ground deformation profile depends on vertical displacement of the bedrock hanging wall, soil thickness, dip angle of the bedrock fault plane, and a shape parameter that is a function of the undrained shear modulus normalized by the undrained shear strength. Validation and consistent agreement are obtained between calculated ground deformation profiles and other independent centrifuge test results and reported numerical data.

Normalized Soil Deformation Induced by Underlying Bedrock Fault

2013 ◽  
Vol 790 ◽  
pp. 150-154
Author(s):  
Qi Peng Cai ◽  
Yun Huang ◽  
Fan Yan Meng
Keyword(s):  
Theoretical Approach ◽  
Ground Deformation ◽  
Error Function ◽  
Hanging Wall ◽  
Vertical Displacement ◽  
Soil Deformation ◽  
Vertical Displacements

Prediction of subsurface ground deformation during bedrock faulting is important for structures located at potential seismic areas. In this paper, a theoretical approach was developed based on error function. Settlement profiles are found to be well represented using error function. Normalization issues of settlement profiles are discussed and it is found that the vertical displacements can be normalized with vertical displacement of the bedrock hanging wall h.

Validation of Coupled FDM-DEM Approach on the Soil-Raft Foundation Interaction Subjected to Normal Faulting

2021 ◽  
Author(s):  
Fang Ru-Ya ◽  
Lin Cheng-Han ◽  
Lin Ming-Lang
Keyword(s):  
Active Fault ◽  
Ground Deformation ◽  
Numerical Models ◽  
Hanging Wall ◽  
Normal Fault ◽  
Small Scale ◽  
Foot Wall ◽  
Normal Faulting ◽  
Raft Foundation ◽  
Overburden Soil

<p>Recent earthquake events have shown that besides the strong ground motions, the coseismic faulting often caused substantial ground deformation and destructions of near-fault structures. In Taiwan, many high-rise buildings with raft foundation are close to the active fault due to the dense population. The Shanchiao Fault, which is a famous active fault, is the potentially dangerous normal fault to the capital of Taiwan (Taipei). This study aims to use coupled FDM-DEM approach for parametrically analyzing the soil-raft foundation interaction subjected to normal faulting. The coupled FDM-DEM approach includes two numerical frameworks: the DEM-based model to capture the deformation behavior of overburden soil, and the FDM-based model to investigate the responses of raft foundation. The analytical approach was first verified by three  benchmark cases and theoretical solutions. After the verification, a series of small-scale sandbox model was used to validate the performance of the coupled FDM-DEM model in simulating deformation behaviors of overburden soil and structure elements. The full-scale numerical models were then built to understand the effects of relative location between the fault tip and foundation in the normal fault-soil-raft foundation behavior. Preliminary results show that the raft foundation located above the fault tip suffered to greater displacement, rotation, and inclination due to the intense deformation of the triangular shear zone in the overburden soil. The raft foundation also exhibited distortion during faulting. Based on the results, we suggest different adaptive strategies for the raft foundation located on foot wall and hanging wall if the buildings are necessary to be constructed within the active fault zone. It is the first time that the coupled FDM-DEM approach has been carefully validated and applied to study the normal fault-soil-raft foundation problems. The novel numerical framework is expected to contribute to design aids in future practical engineering.</p><p><strong>Keywords</strong>: Coupled FDM-DEM approach; normal faulting; ground deformation; soil-foundation interaction; raft foundation.</p>

Faulting, doming and basin formation during orogenic arcuation – the case of the Shkoder-Peja Normal Fault System (northern Albania and Kosovo)

2021 ◽  
Author(s):  
Marc U. Grund ◽  
Mark R. Handy ◽  
Jörg Giese ◽  
Jan Pleuger ◽  
Lorenzo Gemignani ◽  
...  
Keyword(s):  
Hanging Wall ◽  
Normal Fault ◽  
Sedimentary Basins ◽  
Vertical Displacement ◽  
Ductile Deformation ◽  
Fault System ◽  
Normal Faulting ◽  
Two Phase ◽  
Brittle Faulting ◽  
Topographic Constraints

<p>The junction between the Dinarides and the Hellenides coincides with an orogenic bend characterized by a complex system of faults, domes and sedimentary basins. The major structure at this junction is the Shkoder-Peja Normal Fault (SPNF) system, which trends oblique to the orogen and is segmented along strike, with ductile-to-brittle branches in its southwestern and central parts that border two domes in its footwall: (1) the Cukali Dome (RSCM peak-T 190-280°C), a doubly-plunging upright antiform deforming Dinaric nappes, including the Krasta-Cukali nappe with its Middle Triassic to Early Eocene sediments; (2) the newly discovered Decani Dome (RSCM peak-T 320-460°C) delimited to the E by the ~1500 m wide Decani Shear Zone (DSZ) that exposes Paleozoic to Mesozoic strata of the East Bosnian Durmitor nappe (EBD). In the northeasternmost segment, the strike of the SPNF system changes from roughly orogen-perpendicular to orogen-parallel. There, the SPNF system has brittle branches- most notably the Dukagjini Fault (DF) that forms the northwestern limit of the Western Kosovo Basin (WKB).</p><p>The westernmost ductile-brittle SPNF segment strikes along the southern limb of the Cukali Dome with an increasing vertical offset from 0 m near Shkoder eastwards to >1000 m at the eastern extent of the dome (near Fierza) where normal faulting cuts the nappe contact between the High Karst and Krasta-Cukali unit. The central segment north of the Tropoja Basin, with several smaller branches changing in strike, has a vertical throw of at least 1500 meters based on topographic constraints. Even further to the northeast, the SPNF system includes the moderately E-dipping DSZ juxtaposing the EBD in its footwall against mèlange of the West Vardar unit in its hanging wall, where offset is difficult to determine. 3 km eastwards, in the hanging wall to the DSZ, the brittle DF accommodates another 1000 m of vertical displacement as constrained by maximum depth of sediments of the WKB.</p><p>Ductile deformation along the Cukali and Decani Domes occurred sometime between the end of Dinaric thrusting and the formation of the WKB. Brittle faulting partly reactivates ductile segments, but also creates new branches (DF) within the hanging wall of the ductile DSZ. These were active during mid-Miocene to Pliocene times as constrained by syn-tectonic sediments in the WKB. We interpret the SPNF system as a two-phase composite extensional structure with normal faulting that migrated from its older trace along the ductile DSZ to the brittle DF as indicated by cross-cutting relations. The Decani Dome, with higher metamorphic temperature conditions than the Cukali Dome, may reflect the south-westernmost extent of late Paleogene extension in the Dinarides. It may be related to other core complexes and possibly to limited subduction rollback beneath the Dinarides (Matenco and Radivojevi, 2012). Extension from mid-Miocene time onwards was probably related to Hellenic CW rotation during Neogene orogenic arcuation, possibly triggered by enhanced rollback beneath the Hellenides (Handy et al., 2019).</p><p>Handy, M.R.,et al. 2019: Tectonics, v. 38, p. 2803–2828, doi:10.1029/2019TC005524.</p><p>Matenco, L.,& Radivojevi, D. 2012: Tectonics, v. 31, p. 1–31, doi:10.1029/2012TC003206.</p>

scholarly journals The Concept of Accuracy Analysis of the Vertical Displacements Gained from the Hydrostatic Levelling Systems’ Measurements

Sensors ◽  
2021 ◽  
Vol 21 (14) ◽  
pp. 4842
Author(s):  
Waldemar Kamiński
Keyword(s):  
Accuracy Assessment ◽  
Theoretical Models ◽  
Vertical Displacement ◽  
Serial Connection ◽  
Vertical Displacements ◽  
Comprehensive Determination ◽  
The One ◽  
The Individual ◽  
Reference Sensor

Nowadays, hydrostatic levelling is a widely used method for the vertical displacements’ determinations of objects such as bridges, viaducts, wharfs, tunnels, high buildings, historical buildings, special engineering objects (e.g., synchrotron), sports and entertainment halls. The measurements’ sensors implemented in the hydrostatic levelling systems (HLSs) consist of the reference sensor (RS) and sensors located on the controlled points (CPs). The reference sensor is the one that is placed at the point that (in theoretical assumptions) is not a subject to vertical displacements and the displacements of controlled points are determined according to its height. The hydrostatic levelling rule comes from the Bernoulli’s law. While using the Bernoulli’s principle in hydrostatic levelling, the following components have to be taken into account: atmospheric pressure, force of gravity, density of liquid used in sensors places at CPs. The parameters mentioned above are determined with some mean errors that influence on the accuracy assessment of vertical displacements. In the subject’s literature, there are some works describing the individual accuracy analyses of the components mentioned above. In this paper, the author proposes the concept of comprehensive determination of mean error of vertical displacement (of each CPs), calculated from the mean errors’ values of components dedicated for specific HLS. The formulas of covariances’ matrix were derived and they enable to make the accuracy assessment of the calculations’ results. The author also presented the subject of modelling of vertical displacements’ gained values. The dependences, enabling to conduct the statistic tests of received model’s parameters, were implemented. The conducted tests make it possible to verify the correctness of used theoretical models of the examined object treated as the rigid body. The practical analyses were conducted for two simulated variants of sensors’ connections in HLS. Variant no. I is the sensors’ serial connection. Variant no. II relies on the connection of each CPs with the reference sensor. The calculations’ results show that more detailed value estimations of the vertical displacements can be obtained using variant no. II.

scholarly journals From coseismic offsets to fault-block mountains

2017 ◽  
Vol 114 (37) ◽  
pp. 9820-9825 ◽  
Author(s):  
George A. Thompson ◽  
Tom Parsons
Keyword(s):  
Upper Mantle ◽  
Hanging Wall ◽  
Large Earthquake ◽  
Western United States ◽  
Coseismic Deformation ◽  
Finite Element Models ◽  
Interferometric Synthetic Aperture Radar ◽  
Normal Faulting ◽  
Gravitational Forces ◽  
Fault Block

In the Basin and Range extensional province of the western United States, coseismic offsets, under the influence of gravity, display predominantly subsidence of the basin side (fault hanging wall), with comparatively little or no uplift of the mountainside (fault footwall). A few decades later, geodetic measurements [GPS and interferometric synthetic aperture radar (InSAR)] show broad (∼100 km) aseismic uplift symmetrically spanning the fault zone. Finally, after millions of years and hundreds of fault offsets, the mountain blocks display large uplift and tilting over a breadth of only about 10 km. These sparse but robust observations pose a problem in that the coesismic uplifts of the footwall are small and inadequate to raise the mountain blocks. To address this paradox we develop finite-element models subjected to extensional and gravitational forces to study time-varying deformation associated with normal faulting. Stretching the model under gravity demonstrates that asymmetric slip via collapse of the hanging wall is a natural consequence of coseismic deformation. Focused flow in the upper mantle imposed by deformation of the lower crust localizes uplift, which is predicted to take place within one to two decades after each large earthquake. Thus, the best-preserved topographic signature of earthquakes is expected to occur early in the postseismic period.

Loading transfer mechanism of a piled raft subjected to normal faulting in sand

2022 ◽  
Vol 12 (1) ◽  
pp. 1-19
Author(s):  
Q. Cai ◽  
B. Xiang ◽  
C. W. W. Ng ◽  
K. S. Wong ◽  
X. Chen ◽  
...  
Keyword(s):  
Finite Difference ◽  
Hanging Wall ◽  
Three Dimensional ◽  
Pile Group ◽  
Transfer Mechanism ◽  
Centrifuge Test ◽  
Fault Rupture ◽  
Normal Faulting ◽  
Compression Failure ◽  
Piled Raft

Although different kinds of foundations have been investigated against an earthquake faulting, the interaction between pile group and dip-slip fault has not yet been fully understood. This letter investigates the interaction between piled raft and normal faulting by means of centrifuge and numerical modelling. In centrifuge test, a piled raft was simulated with a half model for a better observation of fault rupture path under the raft. The loading transfer mechanism was further examined using a three-dimensional finite difference software (FLAC3D). The measured and computed results showed that the piled raft displaced and tilted linearly with the magnitude of faulting. The fault rupture bifurcated into two and diverted towards both edges of the raft. Two types of loading transfer mechanism were identified during faulting. Working load transferred from the raft to the underneath piles, and also from the piles on the side of the hanging wall to the piles on the footwall side, resulting in compression failure of the piles on the footwall side.

scholarly journals Analysis of ground deformation based on GPS in Sanshandao gold mine, China

2018 ◽  
Vol 55 (1) ◽  
pp. 7-14
Author(s):  
Fengshan Ma ◽  
Hongyu Gu ◽  
Jie Guo ◽  
Rong Lu
Keyword(s):  
Ground Deformation ◽  
Horizontal Displacement ◽  
Vertical Displacement ◽  
Mining Area ◽  
Tectonic Stress ◽  
Gold Mine ◽  
Motion Patterns ◽  
Metal Mine ◽  
Risk Areas ◽  
Discontinuous Deformation

Sanshandao Gold Mine is the first and largest mine operating below sea level in China. Mining has been practiced in this region for at least 25 years. In recent years, buildings above the mining area have been extensively damaged. GPS (with 315 monitoring points) was used to monitor the ground deformation since 2009. Ground deformation induced by mining is much more complex in metal mine than that in coal mines due to the well-developed joints, high tectonic stress and several intersecting faults. All of the factors are analyzed in this study. The results show that discontinuous deformation has occurred on the surface because of the sliding to F3 (name of fault), and there are two motion patterns of F3 during the mining process. Additionally, joints in rock masses with steep dip angles contribute to the vertical displacement and joints with shallow dip angles contribute to the horizontal displacement. Meanwhile, high tectonic stress dramatically enlarges the scale of ground deformation, especially with respect to the horizontal displacement. This deformation results in a striped formation of compressed and stretched regions. Additionally, high-risk and potential risk areas are identified in this study. Finally, the successive data measured since 2009 can contribute to a deeper understanding of ground deformation in metal mine.

Further Comments on Pontryagins Maximum Principle Applied to the Profile of a Beam

1968 ◽  
Vol 72 (690) ◽  
pp. 518-519 ◽  
Author(s):  
L. C. W. Dixon
Keyword(s):  
Phase Space ◽  
Maximum Principle ◽  
Velocity Vector ◽  
Error Function ◽  
Bending Moment ◽  
Space Velocity ◽  
Vertical Displacement ◽  
Hill Climbing ◽  
Horizontal Distance ◽  
Basic Assumptions

Following the appearance of my note on this subject in the July 1967 JOURNAL, Professor Hemp kindly pointed out a mistake in one of the basic assumptions. This has led to a recalculation of the results, and the correct results are given below. a width of beam b lower bound on height of beam d upper bound on height of beam E Modulus of elasticity h (x) height of beam at position x H the Pontryagin Hamiltonian i second moment of area=ah3/12 i length of beam M (x) bending moment = rl, r2 non-dimensional length parameters p density al lengthparam t non-dimensional length parameter=x/l u non-dimensional length parameter=h/l x horizontal distance from base of beam y (x) vertical displacement of the centre-line of beam Y error function in hill climbing sequence Vectors f phase space velocity vector =dX/dt P adjoint vector X non-dimensional state vector

Uplift tests on full-scale pipe segment in lumpy soft clay backfill

2016 ◽  
Vol 53 (4) ◽  
pp. 578-588 ◽  
Author(s):  
R.P. Chen ◽  
B. Zhu ◽  
W.J. Ni
Keyword(s):  
Shear Strength ◽  
Soft Clay ◽  
Vertical Displacement ◽  
Undrained Shear Strength ◽  
Full Scale ◽  
Scale Model ◽  
Pressure Transducers ◽  
Pipe Segment ◽  
Clay Ground ◽  
Undrained Shear

Upheaval buckling of pipelines caused by thermal- and pressure-induced loading is an important issue in pipeline design. The uplift capacity of pipelines is determined by the pipe–soil interaction during pipeline upheaval in soil. Pipelines to be installed in soft clay are usually placed into trenches and then backfilled. In this paper, a set of test devices were developed and a series of full-scale model tests were carried out on a pipe segment buried in lumpy soft clay backfill, including backfilling tests, load-controlled uplift tests, and a displacement-controlled test. Eight total pressure transducers were embedded in the wall of the pipe segment to measure soil pressures on the pipe segment, and five linear variable differential displacement transducers (LVDTs) were arranged to record the vertical displacement of the pipe segment and the surface of the soft clay ground. The stabilizing force keeping the pipe segment in place during the backfilling process was found to fit a nearly linear relationship with the dimensionless undrained shear strength of soft clay. The variation of soil pressures on the pipe segment during uplift loading was significantly affected by the buried depth of the pipe segment and the undrained shear strength of the soil. For all present load-controlled tests in lumpy soft clay backfill, the test ultimate uplift resistances were only about 19%–81% of the results calculated by the Det Norske Veritas approach. Mainly due to the voids’ compression, shearing and strain softening of lumpy soft clay backfill, the difference between initial and stable displacements in a loading step for a load-controlled test or initial and stable loads in a displacement step for a displacement-controlled test is remarkable. The limits of uplift resistances are recommended for the instant and sustaining behaviors of the pipe segment, respectively.

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